Student Guest Blog Post: Drawing Mandalas with Compasses and Protractors! Geometry Art!

Here is the first guest post from my student Morgan! Morgan was in my Honors Problem-Solving Seminar class, and her final project was to learn how to draw a mandala using math! Enjoy! For the rest of the posts, visit: sasproblemsolving.blogspot.com

Hi! My name is Morgan, and because of my love for yoga, I decided to learn how to draw a mandala!

Mandalas represent an imaginary place that one's mind travels too when he or she meditates. Each object one observes in that place has significance, embodying an aspect of wisdom or reminding the meditator of a guiding principle. The mandala's purpose is to help transform ordinary minds into enlightened ones and to assist with healing just as yoga has for me with anxiety. The different movements and yoga positions leave me feeling relaxed and allow me to clear my mind. I felt a similar feeling of relaxation when I drew my mandala.

Having never drawn a mandala before, I had predicted it to be a long, complicated process that would be draining. However, I felt calm and stress-free as I allowed my mind to unravel and draw my mandala. At first, it was a little challenging to know what shapes and lines to draw after I had created the skeleton of the mandala, but by the end, I didn't even have to think much. I went with my intuition and let my mind do what it felt in the moment.

Here is a video of my first mandala drawing, showing the whole process and what goes into creating a mandala.

My first mandala completed

A close up shot of my mandala

Materials needed to draw a mandala:

• Compass
• Protractor 
• Ruler 
• Pencil
• Black pen with felt tip (thin sharpies will do)
• Blank notebook or 8.5 by 11 sheet paper

Procedure:

1. Draw “skeleton” in pencil.
• As I showed in my video, use your compass to draw a small circle in the center of the paper then continue outward drawing circles until you reach near the end of the piece of paper. 
TIP: rotate the paper while using the compass as shown in this video. 


• Once your circles are complete, use your ruler to draw straight lines to divide the circle up into several different sections. 

22.5 cm trick shown above
• In addition, although I didn't show it in my video, you can use a protractor and make markings at every 22.5 cm then use a ruler to draw lines so that your mandala is more precise.
• Also, the circles do not need to be exactly the same amount apart from each other. It actually comes out better if you organically draw some circles close together and and some further apart. 
2. Then begin using your black felt tip pen (or Sharpie) to draw the mandala. 
• Some commons designs and shapes include:
• Petals 
• Longer and thinner
• Shorter and rounder
• Triangles
• Various line lengths 
• Circles with dots 
• Squares 
• Symbols such as: 
• Flowers
• Suns
• Moons
• Trees
  
  Basic designs
• Tip: Begin with drawing simpler shapes then use dots and smaller designs to fill in shapes and the areas surrounding them!
3. After you finish drawing and designing with the black felt tip pen, erase the pencil marks underneath and admire your mandala! 
• You can also add color to your mandala to brighten it up if you want!

After learning how to draw a mandala, I shared the process with some students who are part of Saint Andrew's Mu Alpha Theta, which is a math club at my high school. Here below are some photos of them and their mandalas.

Designing the mandala

Beginning the design after creating the skeleton

Working on the first step with compasses

A colorful mandala!

A finished mandala with a unique design: a different design for each half

Another finished mandala

I hope my blog inspires you and teaches you about mandalas! I have linked some mandala designers and tutorials that I found helpful below as resources for you. :) 

Here are some accounts that I found inspiring when creating my mandala!
@courtneybetts was super helpful in getting me started with my mandala and giving me tips. She has a super cool art Instagram story on her page that features beautiful mandalas. I came across @mandalabybhagya 's Instagram page when looking for inspiration for designs for my mandala. She has lots of intricate colorful mandalas, too! 

One of @mandalabybhagya's colorful mandalas

Another one of @mandalabybhagya's beautiful creations

Lastly, here are some tutorials that I recommend to help you on your mandala journey!
https://www.youtube.com/watch?v=OiSzGBguPm0
https://www.youtube.com/watch?v=QcHDIK0E5KY&t=573s

Thanks for reading! :)

Problem Set 2 for my Problem-Solving Course

I've posted problem set 1 here and Chapter 0, which I've renamed Unit 1, here. Both are going to be part of a workbook I am creating for my students in my Honors Problem-Solving seminar. Thanks a million to @mrdardy for catching some typos and asking me great and thoughtful questions!


Here is my Problem Set 2.

In the 6 problems I give each week, I’m trying to include (and this has pretty much been in my head till now…I blogged about some of it, or wrote in the comments):

-one algebra problem

-one geometry problem

-one probability problem

-one problem based on what I will be doing in class that week

-one problem that may “recur” that they could see again somehow (like, my second problem set has a geo problem that ends up being the golden ratio)

-one logic problem

I think I have to write my weekly unit 2 before I create the next problem set, so it will all fit in well together...in other words, the unit and the problem sets kind of go hand in hand. 

Speaking of hands, below is the logic problem from problem set 2. 

Any feedback is welcomed :)